Derivative Concepts and Applications

Derivative Concepts and Applications

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Hard

Created by

Emma Peterson

FREE Resource

The video tutorial explains how to find derivatives using the chain rule. It covers two examples: the first involves a composite function with a power, and the second uses a rational exponent. The tutorial emphasizes identifying the inner function and applying the chain rule to find the derivative. It also demonstrates rewriting expressions with rational exponents and provides equivalent forms of the derivative using square roots.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in applying the chain rule to find the derivative of a composite function?

Identify the inner function

Differentiate the inner function

Identify the outer function

Differentiate the outer function

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the first example, what is the inner function identified for the derivative calculation?

5x^2 + tangent X

2x^2 + Cent X

x^3 + 2x

cotangent X

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of 2x^2 with respect to x?

4x

8x

2x

x^2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the square root of a function expressed using rational exponents?

Exponent of 1/2

Exponent of 1/3

Exponent of 2

Exponent of 3

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the second example, what is the inner function identified for the derivative calculation?

cotangent X

2x^2 + Cent X

x^3 + 2x

5x^2 + tangent X

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of 5x^2 with respect to x?

15x

5x

10x

x^2

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of tangent X with respect to x?

tan X

cosec^2 X

sec^2 X

cot X

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